document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80883>Question 80883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor the polynomial completely\r<BR>\n" );
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document.write( "121rSQUARED-64tSQUARED </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58028 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=58028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=121r%5E2+-+64t%5E2 ALIGN=MIDDLE  ALT=\"121r%5E2+-+64t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem is to factor this expression.<BR>\n" );
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document.write( "The given expression contains the difference of two perfect squares. As such it falls under<BR>\n" );
document.write( "the factoring rule:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2%29+=+%28a-b%29%2A%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2%29+=+%28a-b%29%2A%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By comparing this rule with the given expression you can see that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+121r%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+=+121r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this leads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+sqrt%28121r%5E2%29+=+11r ALIGN=MIDDLE  ALT=\"a+=+sqrt%28121r%5E2%29+=+11r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Similarly:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+64t%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+=+64t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and taking the square root of both sides of this results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%2864t%5E2%29+=+8t ALIGN=MIDDLE  ALT=\"b+=+sqrt%2864t%5E2%29+=+8t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now return to the factoring rule and substitute for a and b using the above expressions.<BR>\n" );
document.write( "When you do you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2811r%29%5E2+-+%288t%29%5E2%29+=+%2811r+-+8t%29%2A%2811r+%2B+8t%29 ALIGN=MIDDLE  ALT=\"%28%2811r%29%5E2+-+%288t%29%5E2%29+=+%2811r+-+8t%29%2A%2811r+%2B+8t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the right side of this equation is the answer you are looking for. <BR>\n" );
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document.write( "Hope this helps you become familiar with the factoring rule for the difference between<BR>\n" );
document.write( "squares. It comes up reasonably often in book problems that you need to be aware of it, and<BR>\n" );
document.write( "the more you see and use it, the more you will tend to remember it.<BR>\n" );
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document.write( "Cheers ...<BR>\n" );
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